In many action games, characters (such as the main character and non-playing characters—NPCs) may enter “cover mode” in which they “take cover” along movable or immovable objects such as walls. This is a special navigation mode during which the character is protected from its opponents while its movement is constrained to follow a cover line that is predefined for each object. As such, when the character moves from object to object in the game while in cover mode, the system renders the character's trajectory, which follows a sequence of straight line movements. Unfortunately, this produces an unnatural, jagged visual effect, which may lead to an undesirable gaming experience.